Microfluidics is an active research area in modern fluid mechanics, with several applications in science and engineering. Despite their importance in microfluidic systems, micro-orifices with non-circular cross-sections have not been extensively investigated. In this study, micro-orifice discharge with single-phase liquid flow was experimentally investigated for seven square and rectangular cross-section micro-orifices with a hydraulic diameter in the range of 326–510 µm. The discharge measurements were carried out in pressurized water (12 MPa) at ambient temperature (298 K) and high temperature (503 K). During the tests, the Reynolds number varied between 5883 and 212,030, significantly extending the range in which data are currently available in the literature on non-circular micro-orifices. The results indicate that the cross-sectional shape of the micro-orifice has little, if any, effect on the hydrodynamic behavior. Thus, existing methods for the prediction of turbulent flow behavior in circular micro-orifices can be used to predict the flow behavior in non-circular micro-orifices, provided that the flow geometry of the non-circular micro-orifice is described using a hydraulic diameter.